Wei CHEN
2018-11-12 08:47:46 UTC
Hi,
I created a free-form SARIMAX models like this:
[image: 1.png]
where, Y(t) is endog, X(t),...X(t-10) are time lagged exogs, C is a
constant level, N(t) is an autocorrelated residual.
Obviouly, it is ax SARIMAX model with exogenous regressors, the ARIMAX
method works and fits well with this free-form model. However, with this
model, we have large number of weights to estimate, from beta(0) to
beta(10) for X(t) term. For sake of parsimony, some time series analysis
and forecast books suggest to use RATIONAL TRANSFER FUNCTION model, which
has less coefficients to estimated and is writen in form as below:[image:
2.png]
B is a backshift notation, equivalent to L(means lag notation) in
statsmodels package's documentation.
Specially for my case, the model with transfer function can be written as:
[image: 3.png]
So, the model is simplified, and therefore there 2 coefficients to
estimated with X(t) term. Is there any method in statsmodel can realize the
distributed lag transfer function model like this?
Thank you.
Wei CHEN
I created a free-form SARIMAX models like this:
[image: 1.png]
where, Y(t) is endog, X(t),...X(t-10) are time lagged exogs, C is a
constant level, N(t) is an autocorrelated residual.
Obviouly, it is ax SARIMAX model with exogenous regressors, the ARIMAX
method works and fits well with this free-form model. However, with this
model, we have large number of weights to estimate, from beta(0) to
beta(10) for X(t) term. For sake of parsimony, some time series analysis
and forecast books suggest to use RATIONAL TRANSFER FUNCTION model, which
has less coefficients to estimated and is writen in form as below:[image:
2.png]
B is a backshift notation, equivalent to L(means lag notation) in
statsmodels package's documentation.
Specially for my case, the model with transfer function can be written as:
[image: 3.png]
So, the model is simplified, and therefore there 2 coefficients to
estimated with X(t) term. Is there any method in statsmodel can realize the
distributed lag transfer function model like this?
Thank you.
Wei CHEN